Statistical control chart for regime identification in volcanic time series

In an important paper, Mulargia et al. (1987) address the importance of quantitative and objective identification of different regimes of a volcano. They develop a procedure based on the two-sample Kolmogorov-Smirnov (K-S) statistic. The K-S test is a general-purpose test that discriminates between two data sets as belonging to two different regimes based on their empirical distribution functions. The empirical distribution function is designed to describe the aggregate behavior of the volcanic activity, and it is constructed from the orders of the length of the collected repose times in each data set. In this article, we use the idea of statistical process control to distinguish between the variation inherent in the observed repose times and the extraordinary variation that signals a real change in the regimes. We construct a table of control limits, and we demonstrate the procedure of regime identification based on a simple control chart. It shows a point outside the control limits almost as soon as the process enters a new regime. The basis of the statistical process control mechanism is a simple Poisson process, which is state of the art. The proposed control charting procedure is an eruption by eruption procedure, which follows the original chronological order of the eruptions. This procedure is applied to the eruptive history of the Mount Etna volcano. The application shows schematically that the procedure presents a visual interpretation of the identified regimes and can be practically translated for tabular or manual use.